A Manhattan hedge-fund honcho accused of trying to bully his wife into a cheapo divorce settlement by threatening to make their sex videos public says the allegations are a lie — and he’s considering suing her for defamation.

“The allegations are completely false,” David Glenn Rucker told The Post. “I have no idea why she would make that up.”

“She” is Lily Shang, Rucker’s Canadian wife of 20 months — and she says Rucker’s the liar.

“David always says what’s in his best interest,” she told the Toronto Star yesterday.

Rucker filed for divorce against Shang in October, and says he thought their early settlement talks had been amicable — until he found out she had filed papers earlier this week accusing him of threatening to post two private “intimate” videos on the Internet if she didn’t bow to his financial demands.

Rucker, 26, said Tuesday’s filing “caught me completely off-guard.”

“I went through all our old e-mails, and there’s nothing that can be construed as me trying to release a sex tape. It doesn’t make sense. I’m just really confused,” he said.